LAWRENCE, Kan. -- James Sims scored twice and Jake Heaps passed for 110 yards and one TD in his much-anticipated debut, leading Kansas past South Dakota 31-14 Saturday night and matching the Jayhawks' entire victory total of 2012.

His yardage may not look impressive. But Heaps displayed a strong arm and a quick release in his first action since transferring from BYU, where he smashed most freshman passing records, and sitting out last season while the Jayhawks sank to 1-11 in Charlie Weis' first year as coach.

He was 10 for 20 and several of his misses probably could have been caught. The Jayhawks (1-0) rushed for 280 yards against the lower-division Coyotes (1-1) with Sims going 94 yards on 16 carries.

On one especially memorable play for long-suffering Jayhawk fans, Heaps hit Justin McKay with a five-yard touchdown pass -- the first scoring catch by a Kansas wide receiver since Oct. 22, 2011.

Josh Vander Maten was 8 for 18 for 67 yards and one touchdown for South Dakota. He also had 78 of the South Dakota's 219 yards rushing.

Sims, who lead Big 12 runners in rushing in conference games last year, scored on a one-yard run in the second quarter and a six-yard burst around left end in the third. Darrian Miller had 72 yards on 14 carries, including two 17-yard scampers in the 71-yard touchdown drive that put Kansas ahead 21-7 in the third quarter.

At kickoff, it was a sweltering 97 degrees in this rain-starved corner of the Midwest. The Coyotes, looking to snap a 15-game road losing streak, took a 7-0 lead on Vander Maten's 2-yard TD pass to Drew Potter, who sneaked out of the backfield unnoticed and was all by himself in the end zone. Jordan Roberts picked up 14 yards on a counter play and then Vander Maten ran 13 yards to the 2.

Heaps, seeing his first action since Nov. 19, 2011, made his first long connection when he rifled a 25-yard pass to Tony Pierson in the second quarter. A moment later, Josh Ford appeared to make the first TD catch by a Kansas wide receiver since 2011 when he took a short pass and broke several tackles while leading across the goal line. But replays nullified the score and put the ball on the 1, setting up Sims for the score.

Keon Stowers, intercepted Vander Maten's pass late in the second quarter and, picking up blocks, the 298-pounder rumbled 42 yards into the end zone with the first interception by a Jayhawk defensive lineman in 45 games. But a penalty for blocking in the back brought the ball back and moments later, Sims' fumble was recovered by South Dakota's Aaron Swift on the 2.

But the Coyotes failed to pick up a first down and a line drive punt out of their end zone was returned 29 to the 9 by Connor Embree. One play later, Heaps drilled a 5-yard bullet to McKay in the end zone for the Jayhawks' first scoring pass to a wide receiver in 17 games.

The Jayhawks' third TD came on a 12-play, 71-yard drive that was entirely on the ground. Sims went around left end for a 21-7 Kansas lead with 7:34 left in the third.

Vander Maten kept a drive alive with a 37-yard third-down pass to Tyson Graham Jr., and then capped the drive with a 9-yard run. Kansas' Brandon Bourbon scored on an 8-yard run with about 6 minutes left in the fourth quarter.